The Claude subscription does not include Claude API usage.

Claude behaves in Claude Code somewhat differently vs other coding harnesses (sometimes it's a remarkable improvement) connected directly via api. Also, it cost more than the subscription. There's quite a bit of baked in tooling and assumptions in Claude code that may be good for you, or unhelpful based on what you are doing.

Minor correction: the $20 Claude subscription doesn't include API usage, but the $100 and $200 subscriptions include a corresponding amount of monthly API credits.